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/sci/ - Science & Math


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11053409 No.11053409 [Reply] [Original]

talk maths, formerly >>11043085

>> No.11053421
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11053421

>posting the edit

>> No.11053422

>>11053421
Why the racism?

>> No.11053562
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11053562

>>11053409
SShhhh trannies and diversity for category theorist.

Please don't mess up, every diversity thing must be isolate in cat theory people.

>> No.11053563
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11053563

>>11053562

>> No.11053569

>>11053422
Why do you hate Perelman?

>> No.11053579

>>11053562
wow nice lipstick

>> No.11053582

please don't let /mg/ become /pol/

>> No.11053584

>>11053582
/mg/ is a liberal thread. berniebros only.

>> No.11053585

>>11053562
>applied category theory
that actually sounds interesting

>> No.11053588

i can't figure out calculus
halp
is there a calculus book for actual retards

>> No.11053592

Tell me about sci fi math, what will mathematics look like in 2060?

>> No.11053593

>>11053592
nobody will need math in 2060 because we will have been domesticated by our AI overlords
in the beginning was man, and he created God in his image

>> No.11053594 [DELETED] 

>>11040680

>> No.11053597

>>11053588
>>11040680

>> No.11053600

>>11053585
http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf

>> No.11053605

>>11053592
>Linear spaces,topology,set theory?
>Oh yes, Today everything is anabelian, teichmuller spaces,topos and homologies.

>> No.11053617
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11053617

>>11053588
>Calculus for Actual Retards
Fuck, that would sell like hotcakes. I should write it.
>>11053605
>what's your research area
>oh, I study anabelian ring spectrum-valued cohomology of moduli of Teichmuller spaces over Riemann surfaces describing the deformation of solutions of bidimensional PDEs through the h-principle. There's a dude who's made up a program to use it to prove Riemann's hypothesis.
The future looks bright.

>> No.11053643

>>11053409
Isn't Yau a piece of shit? He talked shit about Perelman and downplayed his Poincare conjecture proof.

>> No.11053666

Wasn't Yau acting like a mathematical pirate with his grad students being bandits that steal other people's work and attempt to repackage it as something original?
Didn't they attempt that with Perelman's proof? How utterly Chinese of them.

>> No.11053672

>>11053643
>He talked shit about Perelman and downplayed his Poincare conjecture proof.
based

>> No.11053686

>>11053409
How hard is the Putnam exam and what material would I need to know to even get one of the problems correct?

>> No.11053692
File: 90 KB, 800x592, Grothendieck-Riemann-Roch.jpg [View same] [iqdb] [saucenao] [google]
11053692

>>11053421
Is this what Grothendieck feared?

>> No.11053698

>>11053686
https://www.springer.com/gp/book/9780387684451

Analysis,geometry,algebra, combinatory and very basic number theory.

>> No.11053700

>>11053617
woah, my thesis was on teichmuller spaces over riemann surfaces! but i was looking at diffusive tridimensional pde, where the h-principle only applies to the euclidean case (up to conformal mapping of course)

>> No.11053702

>>11053686
literally high school math
if you want to do the harder problems you need a little basic group theory and analysis
check out the past problems https://kskedlaya.org/putnam-archive/

>> No.11053703

How long does /sci/ typically study?

>> No.11053705

>>11053703
4-8 hours usually uninterrupted when i do get the chance, speed, nicotine, coffee make this easy

>> No.11053706
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11053706

>>11053703
>he ""studies""

>> No.11053709

>>11053706
My memory isn't the greatest so it takes a few rounds to make things stick

>> No.11053710

>>11053703
16 hours a day

>> No.11053711
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11053711

Reminder to work with physicists.

>> No.11053713

>>11053711
no.

>> No.11053726

>>11053709
You don’t need to memorize. Just read it, understand the statement and proof and come back to it whenever you need it.

>> No.11053737

>>11053726
>Just read it, understand the statement and proof and come back to it whenever you need it.
So... study?

>> No.11053738

>>11053711
>reminder to work with pseudo-mathematicians
No

>> No.11053739

>>11053737
on your first pass, this should have been done already. learning isn't studying.

>> No.11053741
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11053741

>>11053422
>Why the racism?

>> No.11053745

>>11053700
Heh, nice job doxxing yourself kid.
I'll show up at your house and discuss complex geometry with you, faggot.
>>11053703
Really depends on how tired I am.
>>11053726
Imagine having the time to do that.

>> No.11053792

>>11053741
why are you here? this is a math thread.

>> No.11053833
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11053833

Can someone here explain the Legendre sieve to me and a simple application of it? I understand the traditional Sieve of Erasthones, so it would be much appreciated if you connected it to that. Thank you

>> No.11053834

>>11053584
lmao yea right s.0.y tits. /mg/ has always been a fascist general

>> No.11053871

What’s that type of graph that starts out as a sine like wave that begins to rapidly oscillate and becomes undefinable?

>> No.11054026

>>11053871
sin(1/x) does that when you get close to 0

>> No.11054039

>>11053588
try apostle calculus

>> No.11054060

>>11054039
try ending yourself

>> No.11054063

>>11053871
topologist's curve?

>> No.11054108
File: 90 KB, 369x475, collid books_covers_0&isbn 9780262514293&type .jpg [View same] [iqdb] [saucenao] [google]
11054108

>In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.

>> No.11054117
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11054117

>>11054060
I can't tell if you're mad because you're an Apostle cock sucker cultist or upset I recommended a retard level book you find too hard.
If you want a real recommendation read Simmons, if you're really a cultist then remember that calculus is retarded and everyone should skip straight to analysis.

>> No.11054152

how do i learn trig/precalc in 2 months while going to school full time and working ~30 hours a week?

>> No.11054464

Fugg bros, I thought I had tensors/tensor fields in the bag till I realized a problem. In physics, it is standard to "prove" that the inertia tensor transforms as a rank (2,0) tensor, i.e. as a billinear form. But the problem is that such tensor is defined as what looks as a linear map in principle, because it is a linear transformation that takes the angular velocity and gives you the angular momentum. However, it seems that this comes from the fact that the angular velocity and angular momentum are "axial vectors", which are the cross product of two vectors, so I hope this transformation rule comes from this fact. I think this can be formalized using the hodge dual for [math]\mathbb{R}3[/math] but I don't see how to formalize it properly.

>> No.11054471

>>11054464
should probably read a book instead of begging for people to spoonfeed so you never learn anything and continue to persist as a helpless tard.

>> No.11054476

>>11054464
damn, i was so ready to post my new tensor explanation screencap but i think you already get it
one of those is probably just a secret linear functional

>> No.11054671
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11054671

>>11053792
>this is an implicitly white, male, high-IQ thread
>asians welcome too

>> No.11054675
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11054675

how do I save the reputation of my field from these ...women.

>> No.11054679
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11054679

>>11054675
>>11053563
>>11053562
Makes sense.
>can't do actual maths
>become the perpetual "undergrad cat theorist"

>> No.11054680

>>11054675
Is it worth it? Can't you just abandon ship for some close-lying part of logic or CS?

>> No.11054736

>>11054675
I want to stab bitches like this

>> No.11054745

>>11054680
I'm just posting what I saw on those twitter accounts to engage in meme culture.

I'm not a student anymore and so I don't need to make any choice like that. Besides, there's no reason to abandon it.
In CS, there's no reason to abandon a language that has advantages and that fits with other descriptions on the side. And those Scala kids aren't contributing to category theory and so their fad will fade.

>> No.11054749
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11054749

>>11054675

>> No.11054766
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11054766

Oh wow, I normally don't follow twitter, interesting browse through these recent threads now.
Didn't know Lurie cucked Beaz out of higher categories

>> No.11054768

daily reminder that FUCK the axiom of choice and FUCK everyone who uses it

>> No.11054777
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11054777

>>11053409
>Yau edition

Reading his popsci book right now. Probably the best popsci book I ever read. One of a few with proper balance between being readable while not simplifying too much.

https://www.goodreads.com/book/show/8174588-the-shape-of-inner-space

>> No.11054796

>>11054777
honestly, the only thing he should have done after that situation with Peri is slit his own belly and die

>> No.11054798

>>11054796
what situation?

>> No.11054805

>>11054749
But nothing in mathematics is "true", in as much as there is nothing in the real world I can point at and say, "behold, mathematics", since there is no such thing as a real circle.

Any and all mathematics happen in the mind. Not really in the mind of one particular person, but as an abstraction that you can only "visualize" in your brain. Drawings, etc, are (useful and powerful) representation, but the "real" math is in your brain.

>> No.11054835

>>11054798
he claimed Perelman's results as his own and because of that Perelman quit maths

>> No.11054836

>>11054831

>> No.11054846

>>11054766
>switching fields because you don't want to read ~800 pages that you have perfectly good intuition and motivation to grasp without much effort
Jesus Christ.
>>11054835
I don't think he quit maths, he probably just quit publishing.

>> No.11054873
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11054873

>>11054836
sorry

>>11054846
>to grasp without much effort

>> No.11054879

>>11054846
even if you are correct quitting publishing is effectively the same as quitting maths

>> No.11054884

What are the best 1-year master degrees in mathematics that you know of? I'm looking at Cambridge part 3 and even though I think I have a shot at getting in, I wouldn't want to just apply to part 3 and then be suicidal for a whole year should they not accept me. What are some good alternatives? It has been a blow learning that many universities like Harvard don't even offer masters and many who do offer 2-year masters instead of 1 year.

>> No.11054890

>>11054671
east asians are honorary whites

>> No.11054895

>>11054890
No, east Asians are the cum receptacles of the failed white men who couldn't get their own race to fuck them. Yes, in a few generations east Asians will be white, but they will have come from the lowest of whites. They will be deformed monsters unable to pick-up white women.

>> No.11054897

>>11054884
>What are some good alternatives?
Don't be suicidal if you don't get into your reach program.

>> No.11054902

>>11054897
I won't literally be suicidal but I just want to know what else is out there. Everything seems to either not exist or to be 2 years long, which is boring.

>> No.11054918

>>11054902
Are you looking at https://www.maths.cam.ac.uk/postgrad/part-iii/prospective.html
?

If you're coming from outside Cambridge, you get a Masters in Advanced Study, not Math.

>> No.11054927

>>11054918
I don't really care about the title, I know the MASt is just a technicality as the classes are the same.

>> No.11054947

>>11054675
so why does category theory attract trannies and twitter fags?
t. sophomore

>> No.11054962

Relatively easy to get into and quickly rewarded with jargon that impresses the uninitiated. Trannies are narcissistic, even in their fetishes, hence the autogynephilia.
Another factor is that the functional programming community had been colonized by trannies. In those communities category theory acquired the reputation as super esoteric and expert-only-affair, so they learned it to show off and are now colonizing category theory itself.

>> No.11054963

Any advice on how to understand the proofs the professor writes in the lecture?
Im just going trough the linear algebra 1 lecture notes and I have a hard time really understanding them. As in it makes sense in the end, but I dont really know what and why he was doing.

>> No.11054965

>>11054947
You know, I didn't realize until yesterday when I went to a talk given by some category theory girl and it was so infuriating because she wouldn't stop talking about "angry people on the internet" and "white males bad" even though it had nothing to do with math. And now that you mention this, I really do wonder what is it about category theory.

My theory is that the true problem is in category theory. Category theory is so esoteric that the only people who focus on it are the kind of people willing to just mind-jizz for months on a piece of paper. What does this sound like? Twitter fags who love to mind-jizz all over the internet.

>> No.11054966

>>11053588
Calculus for Dummies and the Manga Guide to Calculus

>> No.11054969

>>11054963
Don't bother about learning "why" he was doing it. You'll learn more when you take a formal logic course but here is the short story:

The proofs you are seeing are actually fake. Linear algebra was already actually developed out of pure intuition for over thousands of years. Back in the day we even used to have separate matrix theories and determinants theories. It was way way way later that people realized that all of this block-manipulation could actually fit into one theory, and then someone made up the axioms. But notice that they made up the axioms already knowing what the theorems needed to be! This means the axioms are actually reverse-engineered, and so are the proofs.

Why does the professor start proof a certain way? Because the people who originally wrote that proof already knows the theorem they wanted to proof, and just reverse-engineered it. It's not much deeper than this. Don't worry too much about it, but try to learn some of the patterns in case you have to prove some of the initial stuff in a midterm. (By initial stuff I mean anything before K-linear forms).

>> No.11054971
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11054971

>>11054947
>>11054965
see >>11054962
Functional Programming was already taken over by trannies/sissies/"commies". A dialogue between category theory and functional programming circles was opened; mathematicians are neutral on these issues, while trannies are aggressively ideological. Game theory favors the aggressive, even if a minority. Given enough time, they will continue to impose their rules of conduct, and spreading their cumbrain mentality which sissifies everyone, some are even literally turned into sissies and trannies.

>> No.11054976
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11054976

>>11054947
Some strong type systems behave like a (non-extensive w.r.t. functions) category of sets and when you code up a transformation of types (e.g. take any type (string, integers, etc..)), the natural thing to do is add a transformation of functions (e.g. if you code up the function mapping words to their character length, this induces the code that takes a list of words and returns the list of their lengths.

Haskell is a 80's language, made by academics to study lazy evaluation, i.e. collect expression and reduce them only when you need them/as late as possible.
It started to make functors (in the above sense) a core class of transformations in their language when they introduced the IO functor to improve purity (you code up a pure system without user interaction and only at the end map the whole code to a code that does interact with the human - that's the IO monad, which is a functor)

This was then adopted by other language, say Scala and some functional dialects. Earlier this decade, self tough CS fags somehow mistakenly came to think any algebra is "category theory" (search for posts talking about how cateogry theory is hard, and then posting their modular arithmetic book exercises). Even more recently, this "category theory" has become a way to pitch startups (see Weinstein type math-is-awesome Start Trek autists)

Those "applied category theory" people also get validation by hybrid og bloggers like Beaz, sadly.
Nice story, isn't it.

The twitter Scala trannies won't advance Dependent Type Theory, which is the cool part about this all, so I'm not sure how to feel about it.

>> No.11054980

>>11054976
IO stands for input-output

>> No.11054982

>>11052496
what textbook is this? The proofs look simpler than the one I studied from

>> No.11054986

Is Jacob Lurie a visionary who will lead us into a new golden age of mathematics?

>> No.11054991
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11054991

>I fucking love MATH, Hopf Fibration bro

>>11054986
That will depend on whether the famework solves any problems that are in other fields or longwithstanding.

>> No.11054996

>>11054963
just do the proofs yourself. All your questions will disappear.

>> No.11055016

you faggots can keep arguing about category theory all you want. I'll be over here with my CS degree, making $500k starting while maintaining COBOL systems

>> No.11055043

>>11055016
>CS
not math or science

>> No.11055062
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11055062

>>11055043
More science than you, xir.

>> No.11055129

>>11054982
>the proof is taken from Nagata [7]
The nagata book is Theory of commutative fields

The book I'm reading that is pic related is algebraic geometry by Miyanashi

>> No.11055136

Is it true that string theory solves a number of mathematical inconsistencies of QFT, like, say, path integral becomes finite-dimensional or nothing?

>> No.11055148

>>11055136
Well it's different thing, so the results are different.
Yes, there are some nicer structures involved. After all, it arose by choosing to look at nicer structures, so..

>> No.11055152

>>11055148
Sounds too vague. Anything concrete to say?

>> No.11055155

>>11055136
Yes, but it suffers from the same mathematical "fuzziness" (ie, lack of rigorous proof and relying on renormalisation and similar arguments) than the Standard Model of QFT.
String Theory hasn't yet developed a tool to understand perturabations. Many results of the SM aren't accessible by String Theory yet.

And much more importantly (for any self-respecting physicist), we lack the tools to confirm or infirm the predictions of string theory. The bosons of the SM might be hard to conceptualise, and it's almost certain that they are not the "real" physical nature of things (and instead a mathematical construct), but the model we give to reality works: it predicts things and give us results.
String theory can't do that yet.

>> No.11055169

>>11055155
But isn't there something like a non-perturbative string theory?

>> No.11055185

>>11053692
Did he just permanently BTFO the undergrad Category theorist with that?

>> No.11055189

>>11053726
>You don’t need to memorize
Lol. Did you ever take an exam?

>> No.11055197

>>11055155
>and it's almost certain that they are not the "real" physical nature of things (and instead a mathematical construct)
The believe in "real physical nature" of things is cope. There's no reason to believe that it's not turtles all the way down and you can never map the map to the territory. Everything else is aesthetic make-believe. I mean if you want to think doing physics is more than models making predictions, then do it - but don't teach undergrad that fable.

>> No.11055206

>>11055189
...yes. and?

>> No.11055211

>>11053711
I don't get why this supports working with physicists.

>> No.11055247

can someone tell me how i prove that the sum of
a_i converges (from i = 1 -> inf)
iff sum of
a_i converges (from i = n -> inf)
?

>> No.11055253
File: 163 KB, 600x908, category-theorycels.png [View same] [iqdb] [saucenao] [google]
11055253

>>11053409
This is the average category theorycel

>> No.11055266

>>11055247
Literally trivial.

>> No.11055271

>>11055266
then prove it

>> No.11055273

>>11055253
looks like good banter, in their context

>>11055247
removing the finite sum from the limit candidate in the epsilon-delta summation

>> No.11055277

>>11055273
i.e. going from
|(L)-sum(1 to n)a_i| < eps
to
|(L')-sum(m to n)a_i| < eps
where
L' = L - c
where
c = sum(1 to m-1)a_i

>> No.11055302

>>11054947
This makes me want to gas trannies even more

>> No.11055318

>>11055253
>posting a print of your discussion with your retarded friends on twitter
Fuck off.
>>11055273
>good banter
You can go fuck off along with him.
>>11055247
>>>/sci/sqt

>> No.11055367
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11055367

>>11055318
This is how you lose.

>> No.11055381

>>11055318
>Fuck off.
Do you really need to swear?

>> No.11055422

>>11055197
I don't disagree with you. It is turtles all the ways down, and it is imposing a model to a physical system.
However, most of the fields that do that are able to present some predictions and propose experiments to confirm them. No such thing with String Theory.

>> No.11055428

>>11055367
holy shit. super mutants

>> No.11055475

>>11055422
yeah, I was a bit autistic and selectively interpreted your post

>> No.11055531

>>11055253
>theorycel
What does that mean?
An incel theorizing why communism is correct? Or am I missing something?

>> No.11055554

>>11055367
>Adam's apple of a dude
>that weird no-chin a lot of white women have
how??

>> No.11055574
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11055574

>tfw you want to study ct but you are just eating all the time to drive the starvation induced brain fog caused by your eating disorder away

>> No.11055581

>>11055574
Your a man. Nothing you do will ever change that, not Anime, not HRT not mathematics not eating.

Just go outside.

>> No.11055596

>>11053409
I have seen it mentioned (though cannot find a source) that in the context of HoTT, the Hopf fibration (more specifically the generator of [math]\pi_3(S^2)[/math]) is connected to the interchange law for natural transformations (see pic). Would any high iq anons care to elaborate on this to a brainlet like me?

>> No.11055601
File: 21 KB, 584x351, interchange law.jpg [View same] [iqdb] [saucenao] [google]
11055601

>>11055596

>> No.11055654
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11055654

https://www.codechef.com/IEMATIS1
>IEMATIS1 - International Mathematics Olympiad
>There will be 5 levels and each level will have one question.
>The answers will be integer type and each participant will have three chances to lock an answer for a particular question. After three unsuccessful attempts their id would be blocked and they cannot continue participation.
>Level of question will be of International Mathematics Olympiad(IMO) level.

>> No.11055713

If I throw 5 dice, the probability that at least one of them is 6 is 1-(⅚)5. Now, if I want at least two 6s, is the probability of that (1-(⅚)5)2?

>> No.11055719

>>11055596
what have you tried?

>> No.11055724

>>11055531
what do you think it means? apparently pure mathematicians are the equivalent of incels now, and applied math is woke

>> No.11055726

How do problems with the path integral get resolved in string theory though?

>> No.11055741

>>11055724
>what do you think it means?
I speculated on that and since googling "theorycel" linked me to "Chapo trap house" which is some kind of far left group and "theory" appears to be some communist slag for arguing why they are right (?) I theorized that it was linked to that, but I honestly have no idea.

>> No.11055746

>>11055741
i actually have no clue. i shouldn't pretend i do.

>> No.11055770

>>11055713
we know that the total number of possible outcomes is 6^5. now we only need to count the number of outcomes that involve atleast two 6s. if we fix two dices and require them to be 6s, there are 6^3 possible combinations for the other dices. now we multiply this by the number of possible pairs of two dices, so we have 10* (6^3). now the solution is 10*(6^3)/(6^5) = 5/18

>> No.11055775

>>11055724
By the content of this tweet, it's probably it
https://mobile.twitter.com/nmgrm/status/1039998416699326464

>> No.11055987

>>11055211
me neither, i am just continuing a true and tested /mg/ tradition

>> No.11056061

>>11054965
>Category theory is so esoteric
non-mathematician spotted.

>> No.11056089

>>11055726
>problems
>get resolved in string theory
LMAO

>> No.11056102
File: 1.37 MB, 1140x4777, official mg curriculum.png [View same] [iqdb] [saucenao] [google]
11056102

>> No.11056117

>>11055775
Well, this still isn't a proper definition.
Although I think reading Mishima BTFOing them gives me a certain grasp on their character.

>> No.11056127

>>11055724
>pure mathematicians
Are you suggesting there is any other kind of mathematician?

>> No.11056134
File: 40 KB, 300x272, 300px-Brane-wlwswv.png [View same] [iqdb] [saucenao] [google]
11056134

>>11055726
- A classical particle x(t) (maps in R->R^3, time to space) follows a deterministic motion in Newtons theory.
If you got information of the noise characteristic n(t) of such classical particle in motion, you can propagate your loss of information by wrapping it in a stochastic model (Wiener processes, etc.), i.e. the point motion becomes the evolution of a measurable function / distribution p(x, t).
- Quantum mechanics of point particles is similar to this (except not p(x, t) is evolved but the square root, see Fokker-Planck becomes Schrödinger). The stochastic integrals lead to the necessity ito-like calculus (non-commutation relations), but you can solve things analytically
- QFT takes fields already f(x) (maps from R->(R^3->R^n) (time to space to field value), elements in an infinite dimensional vector spaces) and the "stochastification" leads to ill-defined integrals (of which truncated aspects still give experimental information, however)
- String Theory starts with higher dimensional objects, e.g. closed strings (R->(S->R^3), time to embedding in space) and goes QM, the particle excitation are e.g. kinetic energies of S.
The volume of the thing in space time (pic related) looks like nice field theories, e.g. conformal fields, that have nice quantization properties

>> No.11056147

>>11056127
>Are you suggesting there is any other kind of mathematician?
The applied kind.

>> No.11056159

>>11056147
Why would they be mathematicians? There's nothing mathematical about applying math outside of itself.

>> No.11056169

>>11056159
>Why would they be mathematicians?
Why wouldn't they?

>> No.11056174

>>11056169
Why would they?

>> No.11056182

>>11056174
>Why would they?
For the same reason pure mathematicians are mathematicians.

>> No.11056183

>>11056134
Wanted to add some Wikipedia articles, but there don't seem to be good ones

Here's the general framework for low dimensional QFT's (those that live on the world-sheet if you take the string approach)
https://en.wikipedia.org/wiki/Non-linear_sigma_model
And e.g.
https://en.wikipedia.org/wiki/Two-dimensional_conformal_field_theory
https://en.wikipedia.org/wiki/Wess%E2%80%93Zumino%E2%80%93Witten_model

tl;dr string theory (some models anyway) only have to deal with theories on the sheet (submanifold in spacetime), not with R^4->R^n.

>> No.11056217

>>11056159
it's still math, just different...just different

>> No.11056227

>>11056147
>The applied kind.
no such thing is known to exist.

>> No.11056234

>>11056227
>no such thing is known to exist.
Common examples include Witten and Villani.

>> No.11056236

>>11056182
"pure" mathematicians are mathematicians because their main field of study is "pure" math.
>>11056217
there's nothing "mathematical" about figuring out ways to apply a mathematical fact in some other field.

>> No.11056241

>>11056236
>"pure" mathematicians are mathematicians because their main field of study is "pure" math.
No, "pure" mathematicians are "pure" mathematicians because their main field of study is "pure" math.

>> No.11056243

>>11056234
>Witten
He's a mathematician and a physicist. There's nothing """"applied math"""" about him.

>> No.11056246

>>11056243
>There's nothing """"applied math"""" about him.
He applies math outside of itself.

>> No.11056249

>>11056241
>"pure" mathematicians
That's redundant. Just say "mathematicians".

>> No.11056258

>>11056246
In physics, which makes him a physicist. "applied math" is a meaningless and non-existent field.

>> No.11056262

>>11056258
>In physics, which makes him a physicist.
Physics is a subcategory of applied mathematics.

>> No.11056266

>>11056258
Applied maths are a subset of physics.

>> No.11056274

>>11056262
see >>11056266
>subcategory
No such thing exists in the real world.

>> No.11056277

>>11056274
>the real world
Irrelevant to mathematics.

>> No.11056285

>>11056262
Sorry, that is ill-defined.

>> No.11056286

>>11056266
That's ridiculous. Why would math used to model biology be a part of physics?

Also what is "applied math", for me it starts with things like functional analysis and includes everything that is used by other fields (yes, number theory is applied math too).

>> No.11056289

>>11056286
>Why would math used to model biology be a part of physics?
Biology is applied physics.

>> No.11056295

>>11056159
>There's nothing mathematical about applying math outside of itself.
Are you a retarded undergrad?
Applied math is math which is used outside of mathematics itself, eg. PDEs, Linear Algebra or number theory.
If you are doing research on PDEs you are an applied mathematician.

>> No.11056296

>>11056277
Exactly, applied maths are irrelevant to the truer maths.
>>11056286
>functional analysis and includes everything that is used by other fields
>yes, number theory is applied math too
Number theory and functional analysis are a "maths that can be applied outside of maths", not "applied maths". The latter would mean it isn't a subspace of "maths".

>> No.11056298

>>11056295
>Applied math is math
Wrong. Please try to be more intelligent when using /mg/.

>> No.11056302

>>11056295
>PDEs, Linear Algebra or number theory
so as a number theorist I'm an ""applied mathematician""? cool... where do I apply for the extra applied grants?

>> No.11056303

>>11056289
>Biology is applied physics.
That is false.
Biologists are applying physics very rarely, I do not think you know what biology is.
And even if you were this is irrelevant.

>>11056296
applied math :="maths that can be applied outside of maths"

Nobody has ever used a different definition you retarded undergrad.

>>11056302
In the CS department.

>> No.11056307

>>11056303
>In the CS department.
Use >>>/g/.

>> No.11056312

>>11056307
What?

>> No.11056313

>>11056303
Biologists in their capacity as mathematicians use the deeper side of physics constantly. But you can't expect an unintellegent mongrel to know that.

>> No.11056318

>>11056303
>applied math :="maths that can be applied outside of maths"
What are these maths you speak of? Individual theorems? It makes no sense to say that anyone studying number theory is an """applied mathematician""" merely for studying number theory.

>> No.11056319

>>11056313
>Biologists in their capacity as mathematicians
What does that mean and why does it matter?

>> No.11056323

>>11056318
>It makes no sense to say that anyone studying number theory is an """applied mathematician""" merely for studying number theory.
It actually makes a lot of sense with the above definition as number theory is widely used in cryptography.
Turn your braincells on.

>> No.11056326

>>11056312
What "what"? Excuse me?

>> No.11056329

>>11056303
>applied math :="maths that can be applied outside of maths"
Can you demonstrate the existence of any maths that can't be applied outside of maths?

>> No.11056331

>>11056319
Just bio tryin to look smart

>> No.11056332

>>11056323
>It actually makes a lot of sense with the above definition
Your definition makes no sense (unsurpising for a non-mathematician), because someone can easily be a number theorist and not apply it outside of maths.

>> No.11056334

>>11056319
>What does that mean and why does it matter?
Which part do you not understand?

>> No.11056343

>>11056332
>someone can easily be a number theorist and not apply it outside of maths.
How is this relevant to the definition?

>> No.11056347

>>11056329
>Can you demonstrate the existence of any maths that can't be applied outside of maths?
No, that is left as an exercise to the reader.

>> No.11056348

>>11056329
Literally this. Every form of maths can be applied to reality, using something called Platonism.

>> No.11056350
File: 313 KB, 192x240, noo.gif [View same] [iqdb] [saucenao] [google]
11056350

The fuck guy, for 50 minutes you make a post every 2 minutes about this meta topic. This thread is 1 day old now and 50% is category theory twitter Scala tranny bashing and other derivatives of math elitism that nobdy calls for. How about you post some math and questions an explanations.

>> No.11056354

>>11056332
>someone can easily be a number theorist and not apply it outside of maths
Yes. And someone who works on control theory can also never apply it to anything.
Is control theory therefore pure?

>> No.11056355

>>11056343
The definition would call him an "applied mathematician", because he studies "applied maths", i.e., "maths that can be applied outside of maths".

>> No.11056357

>>11056348
>Every form of maths can be applied to reality, using something called Platonism.
Please prove this constructively before making such bold claims.
Else >>>/lit/ is the place for pseudo philosophers like you.

>> No.11056358

>>11056354
>control theory
You seem damaged. It's not a form of maths, so it's not relevant here.

>> No.11056362

>>11056357
>Please prove this constructively
Platonism requires no constructive proof. Or rather, it is its own constructive proof, as it's self-evident just from briefly looking at the mathematical universe.

>> No.11056363

>>11056347
>No, that is left as an exercise to the reader.
Hence "applied" maths is redundant. Just say maths.

>> No.11056367

>>11056358
>It's not a form of maths
Why not it is basically ODEs but more complex. If that isn't math neither is ODEs and if ODEs isn't math PDEs certainly is neither.

>> No.11056371

>>11056362
Okay, just fuck off to >>>/lit/ for platonism.

>> No.11056374

>>11056367
>Why not
Because no mathematician studies it as their main mathematical subject of choice.
>If that isn't math neither is ODEs and if ODEs isn't math PDEs certainly is neither.
Correct.

>> No.11056375

>>11056363
That is also fair, but not the point of the debate.
The position that the distinction is meaningless seems quite reasonable.

>> No.11056378

>>11056371
Platonism is deeply mathematical. There is nothing literary about it.

>> No.11056380

>>11056374
>Correct.
PDEs aren't mathematics?
Then Analysis certainly isn't either and thus none of the billion subjects connected with it and with that you have left certainly over half of former mathematicians jobless.

>> No.11056381

>>11056350
>meta topic
Because exactly 0 people present here right now are mathematicians.

>> No.11056387

>>11056378
Go to >>>/lit/ for philosophy.

>>11056381
At least 1 person here has a degree, but I suspect that number is also the upper bound.

>> No.11056388

>>11056380
Correct. PDEs aren't maths.
Incorrect. Analyses are maths.
Please be of comparable intelligence when replying to a poster on /mg/.

>> No.11056391

>>11056388
>Correct. PDEs aren't maths.
>Incorrect. Analyses are maths
Why?

>> No.11056392

>>11056387
>At least 1 person here has a degree
that sure isn't you if you think that Zero Equaling One is a true statement, logically speaking.

>> No.11056396

>>11056391
>>11056388
I mean, Integration for example is just a special form of PDE.
If anything PDEs are a generalization of analysis.

>> No.11056401

>>11056392
>that sure isn't you
Well...

>if you think that Zero Equaling One is a true statement, logically speaking
I am too smart/educated to understand that statement.

>> No.11056402

>>11056396
Please be of comparable intelligence when replying to a poster on /mg/.

>> No.11056406

>>11056402
>Please be of comparable intelligence when replying to a poster on /mg/.
We prefer not reducing ourselves to a below-average IQ discussion tier.

>> No.11056409

>>11056381
I guess that's true.
Sad!

I'm interested in the Segal–Bargmann space.
Anybody into this flavour of complex analysis/functional analysis/analytic QM ?

>>11056358
I'd really like to understand e.g. the Algebraic Riccati equation etc. I think the fact that it's not purely studied is that it's framed in terms of matrices and never taken to untracktable spaces as of now.
People instead like to dwell in abstract spaces that might reveal something fundamental.

>> No.11056410

>>11056402
Yeah sorry, replying to idiots only legitimizes them. I should know better, but it is late and I am slightly drunk.

>> No.11056416

>>11056410
>I am slightly drunk
Fucking degenerates (Excuse my French) are not welcome in /mg/. Please vacate the premises immediately.

>> No.11056417

>>11056409
>the fact that it's not purely studied
What is that supposed to mean? The equation by itself is certainly studied abstractly. But usually by people interested in control theory of numerical analysis.

>> No.11056420

>>11056416
>Fucking degenerates
There is nothing degenerate about a little bit of alcohol over a meal with your dad and brother.

>> No.11056422

>>11056417
>people interested in control theory of numerical analysis
What a long-winded way of saying "non-mathematicians".

>> No.11056427

Mathematically why I am always depressed with no motivation even for things I used to love like video games.

>> No.11056428

gotta love all these scare quotes and rhetorical questions
end yourselves. none of you are real mathematicians. you're aspiring undergraduates and first year graduate students.

>> No.11056429

>>11056422
>What a long-winded way of saying "non-mathematicians".
Yawn. Start studying or you won't get your degree undergrad.

>> No.11056432

>>11056427
Because you don't follow the most important advice if "go outside" and "get a life".
I am 100% serious about this.

>> No.11056435

>>11056428
>and first year graduate students
Nope. Since 16 Minutes I am officially a second year graduate student.

>> No.11056438

>>11056432
I have absolutely no interest in such things and am horrible at verbal communication and having conversations.

>> No.11056439

>>11056429
Please don't yawn in this highly intellectual meta-space for discussing highly important issues.

>> No.11056441

>>11056438
Nice. I don't give a SHIT. Kill yourself.

>> No.11056446

>>11056438
>I have absolutely no interest in such things
That's a lie.

>and am horrible at verbal communication and having conversations.
That is irrelevant. And doesn't stop you from going outside.

>> No.11056447

>>11056438
Wow anon. you seem to be such a sophisticated individiual with a deep world view.

>> No.11056450

>>11056439
But ist already 00:19 here? It's getting late...

>> No.11056459

>>11056417
Yes I agree.
By "purely" I just mean studied like other popular fields in pure math (the sort where individual numbers barely appear) are studied: Take the thing, take it into some context where there's only shadows of the things property and raise a theory around it. The algebraic Riccati equation is still treated as a Matrix equation and pure math fags (not including numberics guys here, be that fair or not in terms of nomenclature) don't expect to find something out about math by understanding some old school functionals of matrices better.

>> No.11056463
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11056463

>>11056450

>> No.11056467

>>11056438
are you a Rick and Morty watcher too?

>> No.11056475

>>11056450
Still, you need to restrain yourself from disrespecting this highly intellectual forum in even the slightest way.

>> No.11056482

>>11056467
who isn't

>> No.11056484

>>11056463
Weißt du Hurensohn eigentlich wie groß diese Zeitzone ist?

Sehr schlecht geraten, aber trotzdem richtig.

>> No.11056487

>>11056482
idk, actually intelligant people.

>> No.11056489

>>11056482
that sounds like a [math] \Pi_1 [/math] predicate, which is not going to be easy for me to answer!

>> No.11056490

>>11056475
Yawn (but I put my hand in front of my mouth), sorry for disturbing this intellectual discussion.

>> No.11056516

>>11056484
>But ist already 00:19 here? It's getting late...
>But ist
Bin professioneller Piefke-spotter

>> No.11056535

>>11056516
Von der Autokorrektur verraten...

>> No.11056650

>>11056438
The other anon is right. You should at the very least have friends in your department you can do things with outside of math. Studying 24/7 and having minimal human interaction is terrible for your mental health.

>> No.11056800

>>11056650
>mental health
popsci garbage

>> No.11056942

>>11056446
There's no reason for me to leave my house, and I haven't even spoken to most of my high school friends in 3 years. I rarely have conversations with people daily.

>> No.11056944

What type of calculator do you anons use? Is there any point in upgrading to something that has a computer algebra system? I have a 20-year old TI-86 and it is slow, but am I missing out?

>> No.11056956

>>11056944
>/mg/ maths general
Why would I use one?

>> No.11056966
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11056966

>>11056956

>> No.11056977

>>11056942
https://en.wikipedia.org/wiki/Schizoid_personality_disorder

>> No.11057028

>>11056650
That implies I have a job lol

>>11056977
I do have a voice in my head which is probably why I'm good at solving problems, but I'm not schizo

>> No.11057110
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11057110

I'm not following math general right now, but please make this the image for the next thread. Thank you.

>> No.11057242
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11057242

Is the set of all n x n matrices countable?

My method:
1)Take every natural number as a string and parse the first two digits from the rest
2)this defines the size of the matrix and the rest is the information that fills in the matrix
3)the set is iterated upon and the matrices that dont define a valid matrix are thrown out and shifted down

is there a better way to put N and the set of all matrices in one to one correspondence?

>> No.11057247

>>11057242
what are the entries of the matrix? integers? real numbers?
the set of n x n matrices has the same cardinality as the set from which you pick entries as long as that set is infinite. if the set is finite, well, it's different.

>> No.11057249

>>11057247
counting numbers

is there a better way of demonstrating it then what i did

>> No.11057252

>>11057249
what you did is fine

>> No.11057414

Guys, when I was a bit younger and worse at school I accidentally got pretty bad marks in ODEs and 2nd year algebra, which locked me out of all the 3rd / 4th year extensions unless I retook those classes. Being lazy, I haven't done so, and have proceeded to take classes involving complex analysis, graph theory, game theory, and perhaps most damning, operations research. Whenever I visit a math thread, I find myself increasingly unable to keep up with the contents of the discussions, finding them more and more abstract, less and less familiar. Finding myself muttering things under my breath, horrible things, like "how impractical", or "how would we apply that to real life?".

I've been hesitating to ask, fearing the answer, but I must know, for the sake of my sanity. Am I... god forbid, have I accidentally become a statfag?

>> No.11057453

>>11056942
>There's no reason for me to leave my house
There is and it is to stop you from always being depressed and being alienated from all the things you used to like.
I am 100% serious I know exactly what you feel like.

>> No.11057455

>>11057453
The only things I like are anime and video games

>> No.11057462

>>11057249
>is there a better way of demonstrating it then what i did
Yes. For example the proof "this is trivial" would have been much shorter and just as clear.

Another approach is that it is trivial to see that counting numbers are bijective to ordered pairs (odd/even for example) and by induction bijective to ordered strings of length n x n which are bijective to matrices of size n x n.

>> No.11057466

>>11057455
No, that is a lie you keep telling yourself and it is destroying your life.

>> No.11057573
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11057573

>>11057242
What's not countable is the number of functions from N to B={0,1}, that's writeen B^N (cardinal exponentiation)

But you can take arbitrarily number of slots list like in a matrix row and put in arbitrarily large numbers (that's written w^w, here no such slot list is not unending in itself, but all such lists are in it). Then you can look at arbitrary long listing of such arbitrarily long matrices w^w^w (this is again all the lists of lists of lists of any (fixed) size), and arbitrarily long of those w^w^w^w, and so on w^w^w^w^... And you can take this to infinity. Call this e0. You can add any number of elements to it. You can also take those things and for each create another arbitrary long number, w^e0. You can then go on and iterate this process. w^w^w...^e0. You can also look at e0^e0 and e0^e0^e0 and so on. You iterate this to e1. You can now do all this shit with e1 as well...
This is some ordinal but this is STILL COUNTABLE.
My point is, fixed size rows get you nowhwere on the infinity scale, no matter how you nest them Matrices are super tame.

https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)

Eventually you get to ordinals that aren't countable anymore (in particular, the ordinal that holds ALL countable ordinals, w1), but as a matter of fact you run out of the possibility to describe higher and higher countable ordinals long before that
https://en.wikipedia.org/wiki/Church–Kleene_ordinal
That is to say, there's technically countable ordinals smaller that w1, but for them there's no notation possible.

Btw., if you have no issue with postulating the existene of e0, a countable collection of deep nesting of lows if you will (a sort of infinite tree), then you can get one element in correspondence with any Peano arithmetic proof and by induction proof Peano arithmetic consistent
https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof
(This doesn't fall for Gödels trap since it's not a theory of arithmetic in itself)

>> No.11057585

>>11056942
>>11057455
>There's no reason for me to leave my house, and I haven't even spoken to most of my high school friends in 3 years. I rarely have conversations with people daily.
>no reason for me to leave my house
>I rarely have conversations with people daily
>The only things I like are anime and video games
LMAO and you're seriously asking why you're depressed? like what the fuck do you expect to hear? "mathematically" speaking it's because you have absolutely no life AND you're in deep denial about the importance of it. and I'm not the first one telling you this, so there you go, your /sci/entific answer which you've asked for. now fuck off to /r9k/ and let this thread be about mathematics.

>> No.11057602

>>11054836
>search
>math
Wow, that was hard

>> No.11057610
File: 1.86 MB, 1600x2400, AV0A2259_Annette_Frier.jpg [View same] [iqdb] [saucenao] [google]
11057610

>>11057249
Again, think of trees.
E.g. take n^2 prime numbers p_0,p_1,...,p_n^2 and for each of your matrix entries m_0,m_1,...,m_n^2, consider the number that's the product over all n^2 j's of pj^mj.
Now you embedded all your matrices into N

If you believe in LEM, you can now use

https://en.m.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem

to argue for le existence of a bijection.

But also you could use ordinals and that you can get arbitrarily deep with arbitrary long "rows".
The only thing you can't do is going to infinite objects in their own, like the elements of N->{0,1} which each is an infinite choice in its own

>> No.11057616

>>11054971
>some are even literally turned into sissies and trannies.
Hot

>> No.11057617

>>11057610
Also note that you can consider naturals that are a product of primes which have powers of only primes, iterated. They will also be distinct naturals, but enable you to represent nested trees

>> No.11057625

>>11053562
category theory has the potential to be the purest form of autism, well, maybe second to actually doing axiomatic set theory or cardinal arithmetic or something. no wonder sjws and trannies are getting into this shit. the only way to survive category theory without getting retarded is to simultaneously be grounded by something like topology or number theory or maybe algebraic geometry if it isn't too theoretical.

>> No.11057639

>>11056438
>am horrible at verbal communication and having conversations.
And how do you think you can improve?

>> No.11057758

>>11057466
those are literally the only things I care about though for real

>>11057585
I have other excuses for being depressed now, but yes it was mostly shitposting

>>11057639
I honestly have no interest in improving and doubt I'd be able to get very good at it, I just need to find a wife who also doesn't care for social activity, but does want to mutually jerk off to some hentai sometimes.

>> No.11057859

>>11057758
my goodness, you are even more pathetic than i am
>t. 30 yo boomer, 3 years depression, not doing anything, still have no degree

>> No.11057880

>>11057859
Not really I just need things to get back to normal in my life, will be back at a 9-5 fairly soon in any event.

>> No.11057883

>>11057242
Intuitively, you know it has the same cardinality of the field you are constructing your matrix with.
First, you can think of a n * n matrix as a single n*n vector, since you aren't interested in the group properties of the matrix here.
Then, you could do it recursively. A "1x1" vector is obviously isomorphic to the field in question.

For a 2x1 vector, it's basically the same as saying that Z has the same cardinality as N. Once you've done the 2x1 case, the induction is direct.

>> No.11058106

>>11057616
If only you knew how bad your future is, Proto-sissy. There always is a final coom. It can't go on forever, and when you realize that your entire life was dedicated to a consuming fetish... Well, they kill themselves at 30 for a reason

>> No.11058111

>>11057758
>those are literally the only things I care about though for real
Again, that is a lie. After getting severely overexposed to these things you burned out on them. Monotonous living inherently leads to depression and only making significant changes to your life will make you happy again.

You are like an alcoholic believing that he needs alcohol to be happy, which is nothing but rationalizing his self destruction away in order to be safe in his own bubble.
Trust me, I know how you feel.

>I just need to find a wife
Your current lifestyle is the surest guarantee to avoid all female attention.
You also do not need to "get good" at social interaction, you just need to do it.

Again, you are doing nothing but hurting yourself. Preferring the familiarity of the pain in your bubble over the possible pain of leaving it is pure insanity and a guaranteed way to self destruction.

>> No.11058113

>>11055531
"theory" refers to "critical theory", theorycel is someone devoted to learning that.

>> No.11058114

>>11056350
The math elitism can go away. But the scala/catcel bashing will stay.

>> No.11058118

>a manifold has 3 properties:
>- hausdorff: so any two separate points are >actually separate, you can draw little >neighborhoods around each one which do not >intersect
>- second countable: so there is a sequence of >open sets which can be used to write any >open set via unions (think how any real >number is a limit of rational numbers, and >there are countably many rational numbers)
>- locally euclidean: so at every point there is a >neighborhood which is homeomorphic to R^n >for some n. what this means is that you can >cut out a little ball around any point and >stretch/twist that ball so that it looks like part >of physical n-dimensional space.
>any space like this is a topological manifold
>once you have this last property, you can >define a manifold via an "atlas" of "charts" >which is just a collection of functions between >parts of your manifold and R^n. the functions >should be homeomorphisms and for every >point in the manifold there has to be at least >one function (chart) which takes care of it. it's >just like having flat maps for earth.
>if the charts in your atlas are in fact >differentiable, or more precisely if the >composition of one such map and the inverse >of another as a map from R^n to R^n is >differentiable, then your manifold is a >differentiable manifold. if the charts are >smooth, then you get a smooth manifold.
>if you attach a metric to you manifold (an >inner product in the tangent space at each >point) then you get a riemannian manifold.
In what topology book can I read more thoroughly about (topological) manifolds?

>> No.11058139
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11058139

>>11057110
>https://twitter.com/hashtag/homeworkslave?lang=en
yo wtf

>> No.11058218

>>11058118
Lee's books Introduction to smooth/topological manifolds

>> No.11058221

>>11058118
Lee has a well known series on topological, smooth and riemannian manifolds.

>> No.11058228

>>11058118
to say a different thing, milnor's topology from the differentiable viewpoint book is quite short and good, maybe be a good idea to look over it first

>> No.11058245

>>11058118
Morita's Geometry of Differential Forms is a pretty good introduction to manifolds imho

>> No.11058259

>>11058245
based. It's also very thorough, it proves some things a lot of manifolds books forget to prove, for example the fact that d/dx_i span R^n. In general, it's a great book, highly recommended.

>> No.11058317
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11058317

just started cardinal arithmetic in set theory.

>> No.11058337

How do I into Hodge theory?

>> No.11058340

>>11058337
https://b-ok.cc/book/504403/c11c1e

>> No.11058346

>>11058337
Differential Analysis on Complex Manifolds.

>> No.11058347

>>11058340
>>11058346
>>11058337
Btw I forgot to mention, but I'm especially interested in applications to algebraic geometry, if that might change book rec

>> No.11058427

>>11058347
I'm fairly sure Voisin's book is specifically about Hodge theory in algebraic geometry.

>> No.11058438

>>11058337
http://w3.impa.br/~hossein/myarticles/hodgetheory.pdf

>> No.11058480
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11058480

how do I deal with loneliness?

>> No.11058490

>>11058480
Shitpost on 4chan/twitter and jerk off to anime like me

>> No.11058494

>>11058490
been doing that for years

>> No.11058498

>>11058494
Do it harder then maybe,


or get into erotic roleplaying on f-list.

>> No.11058505

>>11058498
I've done all the degenerate stuff you can think of.

>> No.11058550

>>11058505
then find someone to do degenerate things with IRL or something, go on tinder

>> No.11058692

>>11055581
>just go outside
This is not good advice
>>11055574
Just gas yourself you stupid fuckin tranny

>> No.11058715

How long can you guys keep studying for? Today I went on for ~4 hours with the aid of an espresso after 2 hours. I got myself quite the headache now, hopefully I just have to get used to it.

>> No.11058807

>>11058715
4 hours of intense thinking when solving a problem or 6 hours of full focused study on a good day. All the hours after that are non-productive

>> No.11059057
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11059057

>>11057610
>If you believe in LEM, you can now use

>> No.11059073
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11059073

>>11059057
W H A T

>> No.11059086
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11059086

>>11059073
nobody dosent beleive LEM, thats a meme put forward by radical logical positivists

>> No.11059098
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11059098

>>11059086
>nobody dosent
Are we supposed to interpret this with or without LEM?

>> No.11059122

>>11059086
Mathematics isn't about whether your name is Micheal or whether your name is not Micheal.
It's about ideas expressed by symbols, together with manipulation rules of those symbols that can be communicated by books, in a way that two different people can come to the same formal conclusions, even if they live 100 years apart. Not adopting LEM just means not adopting certain derivation rules. There's no forbidding or enforcing law telling you whether it's right or wrong about adopting or not adopting some axiom about some loosely described type of object, and so there's no reason to assign truth value in either of two options.
Mathematics isn't about whether your name is Micheal or whether your name is not Micheal.

>> No.11059137
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11059137

>>11059098
kek

>> No.11059143
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11059143

>>11059122
>It's about ideas expressed by symbols, together with manipulation rules of those symbols that can be communicated by books, in a way that two different people can come to the same formal conclusions,
*completely btfos your shitty ideology*

>> No.11059157

>>11059143
No, obviously I blow out his.

>> No.11059158

>>11059122
>There's no forbidding or enforcing law telling you whether it's right or wrong about adopting or not adopting some axiom about some loosely described type of object, and so there's no reason to assign truth value in either of two options
thats different then "believing" a meta logical truth. theres no way of even coming to a conclusion of what mathematics is if you dont believe in LEM. If you cant parse all thought of math into A and Not A then how do you even come to a conclusion of what youre doing in terms of strings and symbols?

>> No.11059176

>>11059157
If its only about symbols being manipulated, then why can't we have a system of complete formal axioms for the vast majority of fields?

>> No.11059189
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11059189

>>11059158
Not adopting LEM does not mean
>for all statements A, it's undecidable whether "A or not A" holds
A lot of statements are decidable (You are able to prove that A is true, or that not A is true) and for a lot of statements you can find out whether or not "A or not A" holds.
The modus operandi is collecting statements that are provable. If you want to use that word, you do logic/math and generate statements that are "true". The fact that you can judge "oh, that's a statement I've prove" doesn't contradict that there are statements A out there for which you can't find a proof of "A or not A". I.e. (unless you adopt LEM for all A), there are statements for which "A or not A" isn't provable.

Also, at least in constructive logic, it's noteworthy that for all statements, indeed you can proove that "not(A and not A)" is provable. I.e. the law of non-contradiction holds in even Minimal Logic. Classically, the law of contradiction is equvalent to LEM, but it clearly has different semantics (unless you collapse it, by adopting LEM as an axiom).

It's not like LEM gives you a theory that lets you prove more statements (as seen from the classical perspecitve).

LEM says something about the "truth" of statement (which is a "redundant" notion if you have provability), and that there are only two cases (A is true or not true)
Noncontradition says something about...well contradition: That not two truths apply. Why should those notions be collapsed.
Let excluded middle ("A or not A") be something which has to be established.

>> No.11059227

Hey /mg/. I've pretty removed from math these days but I recently stumbled into the successive discounting problem where you have some percentage discount [math]x[/math] and another percentage discount [math]y[/math] and you want to find the total discount after they are both applied successively. My initial, naïve impression was that the total would merely be [math]xy/100[/math], but working out real numbers that is quickly proven untrue. It turns out the correct expression is

[eqn]
x+y-xy/100
[/eqn]

Can someone explain the intuition/rationality behind this? Even just a hint may help, I don't think I have the correct perspective.

>> No.11059241

>>11059189
This has nothing to do with apodting lem in some structure to study it or something, It's about believing LEM. You are completely missing the point. Show me how what you are saying is even on a solid foundation of you don't even beleive in lem.

>> No.11059253

>>11059227
I guess to clarify what I'm thinking.
Since we know multiplication is commutative, the order we take the discounts in does not matter, hence we have the left side of the expression [math]x+y[/math], but I'm not quite as clear about the right side. Since the discount is successive, we want to remove the total of both discounts taken from the full price, but how does that translate to the product [math]xy[/math]?

>> No.11059263 [DELETED] 

>>11059241
I see. Well I'm not sure propositions are more than a useful tool. If you say "I have a mother", are I and mother etc. all notions that are well defined beyond communication with other humans and reflections in your head? Where do you start or end, is there an essential sense to beings. Seems like few sentences can be said to fundementally hold ground, except for in an operative sense. Statements have a biological point - capturing information and help in doing stuff (conciously or not). Caoutak T Truth of statements seems like a debatable abstraction.

>> No.11059275

>>11059189
you literally aren't answering anything. all you have to do is explain why I should beleive anything you say if you aren't even sure of it, by definition of what you are saying. (namely, you don't beleive LEM exists.)

>> No.11059337 [DELETED] 

>>11059275
>why I should beleive anything you say if you aren't even sure of it
Not sure what you mean by that.
I'm not trying to convince anybody of anything and I don't think I'm unsure about anything.
I'm not sure how to interpret "LEM exists", but I prefer mathematical systems that don't adopt it - because it gives us not much (it gives us shortcuts for proves, but then again it also destroys some axiomatic systems that are in contradition to it).

I'm not realist enough to think we can figure out logical laws that apply to the real world. You cannot know nuffin is only a meme because it's true. That doesn't mean it's not helpfult o act as if reason always applies - after all, we each only have 100 years on this world. Even if e.g. the concept of the "self" is elusive and apriori only has practical value in terms of communicating with others and reflecting on oneself. Not using language - for sake of it not corresponding to anything that will necessary survive our conception throughout the millenia - isn't a solution either.

>> No.11059347

>>11059275
>why I should beleive anything you say if you aren't even sure of it
Not sure what you mean by that.
I'm not trying to convince anybody of anything and I don't think I'm unsure about anything.
I'm not sure how to interpret "LEM exists", but I prefer mathematical systems that don't adopt it - because it gives us not much. LEM gives us shortcuts for proofs, but then again it also destroys some axiomatic systems that are in contradition to it.

I'm not realist enough to think we can figure out logical laws that apply to the real world.
"You cannot know nuffin" is only a meme because it's true (because even two smart humans won't ever agree on all the "fundamental" questions).
That doesn't mean it's not helpfult o act as if reason always applies - after all, we each only have 100 years on this world. Even if e.g. the concept of the "self" is elusive and apriori only has practical value in terms of communicating with others and reflecting on oneself. Not using language - for sake of it not corresponding to anything that will necessary survive our conception throughout the millenia - isn't a solution either.

>> No.11059362 [DELETED] 

>>11059347
that is to say, I think maybe 1921 still had the idea that propositions are something that can capture the world, but irl most statements we utter don't hold ground in the end. If I say "I have a mother", then formulating the sentence has use in communicating with others and for me to capture some information (data uging me to act in some way or another), but that doesn't mean "I" or "mother" has solid real grounding. It doens't mean that it describes an entity - it's only clear that it makes sense to use such language. Giving realism to each and any useful proposition (utterence) seems dubious. Unless you're Russel.

>> No.11059367

>>11059347
that is to say, I think maybe 1921 Wittgenstien (alla https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus)) still had the idea that propositions are something that can capture the world, but irl most statements we utter don't hold ground in the end. If I say "I have a mother", then formulating the sentence has use in communicating with others and for me to capture some information (data uging me to act in some way or another), but that doesn't mean "I" or "mother" has solid real grounding. It doens't mean that it describes an entity - it's only clear that it makes sense to use such language. Giving realism to each and any useful proposition (utterence) seems dubious. Unless you're Russel.

>> No.11059371

>>11059337
>I don't think I'm unsure
You are unsure about everything if you don't beleive LEM. Please point out where I'm wrong about this.

>> No.11059396

>>11059371
I elaborated about this here >>11059189.
LEM says that FOR ALL propositions "A", it's (per logical axiom) true that "A and not A" have the truth value "True".
Even if you don't adopt it, you'll be able to prove, that excluded middle holds for many many propositions.

For a real life example, I might look out of the window and see it's now day. So I establsih that it's day. So I also establish "It's day or it's not day". For a math example, you can prove that "1=1 or 1!=1".
That is to say, just because I don't adopt LEM (excluded middle apriroi being true for all statements), doesn't mean it's not provable for all statements. Indeed, as soon as I have evidence/prove for a stamtenent "B", then "B or not B" is also established.

Moreover, there's nothing I can prove in an axiomatic system with LEM that I can't prove constructively, when viewed from a classical lense. So it's just a cheat code.

>> No.11059403

should have said
"doesn't mean it's - for all statements - not provable"

>> No.11059414

>>11059371
Said differently, adopting LEM means to claim that for all statements A, either establishing A or establishing not A will be the case.
But since there are instances of particlar P where "P or not P" can't be established, this shows that LEM just postulates truth values for such statements that I otherwise have no access to.
Now if it would be just that, then adopting LEM to close up all those holes would be one approach.
But it happens to be the case that there are other (mathematical) axioms that don't go together with LEM and are worth studying, and moreover for any statement "Q", you can prove "not not Q" anyway also without LEM. So why adopt it.

That whole paragrpah doesn't really relate to the realism question btw.
On /mg/ I'm not really interested in post world war philosophy (I know that engineering types feel save to think the world is naturalistic and rational and no thought that can't be put in mathematical terms can have sense or value :P).

>> No.11059459

>>11059414
>>11059396
Again, you are stuck in formal systems. I am taking about laws of thought. You can set up formal systems to emulate weaker systems, but they are ultimately reducible to your own personal laws of thought. Your mistake is thinking that formal symbols actually represent ontological objects in essence. And I guess since you outted yourself as not involved in philosophy it's pointless to continue the conversation because your unconscious formalist philosophy is leaking into your argument.

>> No.11059479

>>11056183
>>11056134
That still doesn't explain exactly how path integration gets mathematically sound in string theory.

>> No.11059517

>>11059459
You don't seem to read my posts, but whatever.
I think we can do formal calculus, popping out expressions after expressions and do formal logic and have fun doing it. I don't think that has to tie to the world.
I don't think logic (especially of this sort) is all that applicable to reality or ontology.
But I don't know how reasoning fundamentally works either. I don't know how we end up making the choice of the systems we want to study in math. Once we got that covered, though, we can do formal math. I don't have the feeling that at this point, judgements of reason are really all that involved in that process. I might well be wrong.

>> No.11059532

>>11059479
It never becomes sound, it just gives more models and in those, you might be able to capture some systems that didn't work in some quantum field theories.
For technicalities of why things work when you do small field theories on worldsheets embedded in space, well then we'd do a lecture.
The first pitch for string theory was when someone wanted to fit some experimental data that have properties like the beta/gamma functions and cooked up some model to make it work, which happened to be a string. So there's some scattering amplitudes that you can get to in the string context, sort of which are more ill defined in a QFT
You can read up on some history of how it came about maybe here
https://en.wikipedia.org/wiki/Regge_theory
But again, it's not like string theory is a nice "closed" framework like...Lie group theory, say.

>> No.11059536

>>11059532
in the history section in that link

>> No.11059553

>>11059532
I definitely remember some anon here said path integrals in string theory become finite-dimensional integrals over moduli spaces or something like that.
My question is actually this: is integration over all possible world sheets mathematically well-defined or is it like the path integration where you need a bunch of crutches just to make it seemingly "work" in some very special cases (when certain conditions on the potential hold etc.)

>> No.11059558

>>11059517
One more time, there are symbols on paper. And then there is the thoughts and objects that we conceive of. Formal systems are just symbols that we operate in accordance with transformation rules. We are trying to emulate our own conceptions with these symbols but we have proved this has limits to it. I am saying that LEM is apriori true. This is intimatley known. What's the point of saying you don't know? That is to imply that there exist some reality apart from your mind. It's pointless to mystify things beyond your comprehension. Also You can create systems that's don't use traditional laws of thought by these are limited in the same way godel incompletneas thereoms show. You are confusing the symbols for what our minds are doing

>> No.11059571

>>11059553
I'm sure there's cases where things get simpler, but string theory is also a vast collection of models and not everything is possible. In particular, as soon as you integrate over 3 or 4 dimensional spaces and need to factor out (homotopically) equivalent typologies, you're faced with extremely hard classification issues that are not readily solved. So you see how it won't all magically work out. Even if there may be nice models where things work - I'm not an expert.

>> No.11059577

>>11059558
>I am saying that LEM is apriori true.
I don't see how the statement of lem holds it's truth in itself. Might be that what you see in Negation is stronger than what I can see about it

>> No.11059586
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11059586

Hey just look at this shit

https://ncatlab.org/nlab/show/Science+of+Logic

>> No.11059676
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11059676

>>11059586
Yeah, Urs is based. I wish he wouldn't do all the "nice" topology stuff in lectures that seem to take him quite away from field theory. But that might be debatable.

Also
https://youtu.be/ARarjQYOhA4

>> No.11059713

>>11059371
>You are unsure about everything if you don't beleive LEM.
Please point out where you're correct about this.

>> No.11059725

>>11059558
>there exist some reality apart from your mind.
That's apriori true. This is intimately known.

>> No.11059866

>guess what, new thread is not gonna be linked here yet AGAIN

>> No.11059879

>>11055129
Thanks

>> No.11060218
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11060218

>>11058106
Ooo, call me a proto-sissy again. That's hotter than the vore I just jerked to.

>> No.11060724
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11060724

>>11053409